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Integrate 3t^2 + 7t with respect to t, between 1 and three.

To integrate you add one to the power and divide by the new power, so this becomes:3t3/3 + 7t2/2 simplifying to t3 + 7/2 t2If we were just performing indefinite...

Answered by Josh M. Maths tutor
2967 Views

Integrate (lnx)/x^2 dx between limits 1 and 5

Let I = integral[(lnx)/x^2 dx] for simplicity.Firstly, we realise we must use integration by parts. This is:Integral [u(x)v'(x) dx] = u(x)v(x) - Integral[u'(x)v(x) dx]So we can see that, by letting u(x)=l...

Answered by Jimmy L. Maths tutor
3178 Views

Determine the stationary points of y=(5x^2)/(lnx)

Differentiate y with respect to x using quotient rule:y'=[(1/x)(5x^2)-(10x)(lnx)]/(lnx)^2 =[5x-10xlnx]/(lnx)^2Stationary points occur when y'=0, so when y'=0 we have:5x-10xlnx = 0x(5-10lnx)=0So x=0 or 5...

Answered by Jimmy L. Maths tutor
3374 Views

Find, using calculus, the x coordinate of the turning point of the curve y=e^(3x)*cos(4x) pi/4<x<pi/2 (Edexcel C3)

The turning point of a curve is the point at which the gradient is 0 as from there it stops rising and starts falling or vice versa. To find this we differentiate y with respect to x (dy/dx) to find the g...

Answered by James W. Maths tutor
13020 Views

State the nth term of the following sequence: 3, 7, 11, 15, 19

First we look at the jump between each term:7-3=4, 11-7=4, 15-11=4, 19-15=4So we know that the difference in each step is 4. So our expression with look like 4n+d for some number d.Comparing what we have ...

Answered by Huw D. Maths tutor
5463 Views

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